Properties

Label 8100.2.ba
Level $8100$
Weight $2$
Character orbit 8100.ba
Rep. character $\chi_{8100}(1619,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $2848$
Sturm bound $3240$

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Defining parameters

Level: \( N \) \(=\) \( 8100 = 2^{2} \cdot 3^{4} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8100.ba (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 300 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(3240\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(8100, [\chi])\).

Total New Old
Modular forms 6576 2912 3664
Cusp forms 6384 2848 3536
Eisenstein series 192 64 128

Decomposition of \(S_{2}^{\mathrm{new}}(8100, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(8100, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(8100, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2700, [\chi])\)\(^{\oplus 2}\)